If you're near LHR, try just swinging past uniform stores and giving it a bash. They'll often try and fit you in if they can. The term "uniform fitting" is a bit misleading. It's more like when you go in to a highstreet store, tell them your sizes, go to a dressing room to try them on and then change them if they don't fit. It takes about an hour - maybe a tad more - but the involvement of the BA staff there is minimal. They just hand you stuff.
So again, if you're nearby and have time to spare, just nip past.